Finite Group Databasebeta

← #34078714

Subgroups — #34078714

Order 19328.

500 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012760C211yesmaximal, characteristic, complemented
2C2×M16×D151C211yesmaximal, characteristic, complemented
3#23752725C211yesmaximal, characteristic, complemented
4#23752722C211yesmaximal, characteristic, complemented
5#23752469C211yesmaximal, characteristic, complemented
6#23752468C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752463C211yesmaximal, characteristic, complemented
9#23752459C211yesmaximal, characteristic, complemented
10#23752458C211yesmaximal, characteristic, complemented
11#23752455C211yesmaximal, characteristic, complemented
12#23752249C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19#18012760—24no—
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic, complemented
22C2×#14558989C2211yescharacteristic, complemented
23C2×#14558988C2211yescharacteristic
24C2×#14558987C2211yescharacteristic
25C2×#14558987C2211yescharacteristic
26M16×D151—24no—
27C2×C8×D151C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012724—21no—
30#18012721—21no—
31#18012719C2211yescharacteristic
32#18012718C2211yescharacteristic
33#18012715C2211yescharacteristic
34#18012714C2211yescharacteristic
35#18012713C2211yescharacteristic
36#18012710C2211yescharacteristic
37#18012709—21no—
38#18012707—21no—
39D4×Dic151—21no—
40#18012701—21no—
41(C22⋊D151)⋊C4—21no—
42(C22⋊D151)⋊C4—21no—
43#18012697C2211yescharacteristic
44#18012697C2211yescharacteristic
45#18012673C2211yescharacteristic, complemented
46#18012670C2211yescharacteristic, complemented
47#18012670C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012663C2211yescharacteristic, complemented
50#18012662C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52#18012660C2211yescharacteristic, complemented
53#18012659C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×M16×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#107×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151D411yescharacteristic
62#14559005—22no—
63#14559005—22no—
64#14559003—22no—
65#14559003—22no—
66C2×Dic302C2311yescharacteristic
67C2×D604—21no—
68C2×D604—21no—
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C22×Dic151—21no—
74C22×Dic151D411yescharacteristic
75C2×C4×D151—22no—
76C2×C4×D151—22no—
77C2×C4×D151—21no—
78C2×C4×D151D411yescharacteristic
79C2×C4×D151D411yescharacteristic
80C2×C4×D151C2311yescharacteristic
81C2×C4×D151C2311yescharacteristic
82#14558994—22no—
83#14558993—22no—
84#14558989—22no—
85#14558988—22no—
86#14558987—22no—
87#14558987—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—22no—
91C8×D151D414yescomplemented
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105C4×Dic151—21no—
106C4×Dic151—21no—
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111SD16×C151—22no—
112M16×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151—21no—
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22×D151—22no—
121C22×D151—21no—
122C22×D151—41no—
123C22×D151—41no—
124C22×D151C2×D411yescharacteristic
125C22×D151C2×D411yescharacteristic
126Dic302—21no—
127Dic302—21no—
128D604—21no—
129D604—21no—
130D604—42no—
131D604—42no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C22⋊D151—42no—
135C2×Dic151—22no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—42no—
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—22no—
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—22no—
146C4×D151—42no—
147C4×D151C2×D412yes—
148C4×D151#4112yes—
149C151⋊C8—21no—
150C151⋊C8C2×D412yes—
151C23×C151—21no—
152C23×C151C2×D411yescharacteristic
153Q8×C151—21no—
154Q8×C151—21no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—42no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2411yescharacteristic
165C8×C151—21no—
166C8×C151C2×D412yes—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151C22×D411yescharacteristic
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—44no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151#12112yes—
184C4×C151—21no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151C22×D411yescharacteristic
189C4×C151C2×#4111yescharacteristic
190Dic151—21no—
191Dic151—41no—
192Dic151—41no—
193Dic151—41no—
194Dic151#12112yes—
195C2×C151—41no—
196C2×C151—81no—
197C2×C151C2×#12111yescharacteristic
198C2×C151#57511yescharacteristic
199C2×C151#57511yescharacteristic
200D151—22no—
201D151—41no—
202D151—81no—
203C151#305411yescharacteristic, complemented, Sylow
204#3054—1511nomaximal, Sylow
205C2×#135—1511no—
206C22×M16—1511no—
207#525—1511no—
208#525—1511no—
209#470—1511no—
210#470—1511no—
211#469—1511no—
212#469—1511no—
213#468—1511no—
214#468—1511no—
215#468—1511no—
216#468D15111yescharacteristic, complemented
217#427—1511no—
218#416—1511no—
219#416—1511no—
220C2×#41—1511no—
221C2×#41—1511no—
222C23×C4—1511no—
223#135—3024no—
224C2×Q16—1511no—
225C2×SD16—1511no—
226C2×SD16C2×D15111yescharacteristic, complemented
227C2×D8—1511no—
228C2×M16—3024no—
229C2×M16—1511no—
230C2×M16—1511no—
231C2×M16—1511no—
232C2×M16C2×D15111yescharacteristic
233C22×C8—1511no—
234C22×C8—1511no—
235#123—3021no—
236#123—3021no—
237C22⋊Q8—1511no—
238C22⋊Q8—1511no—
239C22⋊Q8—1511no—
240C22⋊Q8C2×D15111yescharacteristic
241#121—1511no—
242#121—1511no—
243#121—1511no—
244#121C2×D15111yescharacteristic
245#120—3021no—
246#120—3021no—
247C4×D4—3021no—
248C4×D4—3021no—
249C4×D4—3021no—
250C4×D4—3021no—
251#117—1511no—
252#117—1511no—
253#107—1511no—
254#107C2×D15111yescharacteristic, complemented
255#106—1511no—
256#106—1511no—
257#103—1511no—
258#103—1511no—
259#103—1511no—
260#103C2×D15111yescharacteristic, complemented
261#102—1511no—
262#102—1511no—
263#102—1511no—
264#102C2×D15111yescharacteristic, complemented
265C24—1511no—
266#41—3022no—
267#41—3022no—
268#41—3022no—
269#41—3022no—
270C2×Q8—1511no—
271C2×Q8C22×D15111yescharacteristic
272C2×D4—21no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—1511no—
279C2×D4C22×D15111yescharacteristic
280C22×C4—3022no—
281C22×C4—3022no—
282C22×C4—3021no—
283C22×C4—3021no—
284C22×C4—1511no—
285C22×C4—1511no—
286C22×C4—1511no—
287C22×C4—1511no—
288C22×C4—1511no—
289C22×C4C22×D15111yescharacteristic
290Q16—3022no—
291SD16—22no—
292SD16—3022no—
293D8—3022no—
294M16—22no—
295M16—3022no—
296M16—3022no—
297M16—3022no—
298C2×C8—3022no—
299C2×C8—1511no—
300C2×C8—1511no—
301C2×C8—1514no—
302C2×C8C22×D15111yescharacteristic
303C2×C8C22×D15111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—3021no—
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—1511no—
309C4⋊C4—1511no—
310C4⋊C4C22×D15111yescharacteristic
311C4⋊C4C22×D15111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C42—3021no—
323C42—3021no—
324C23—21no—
325C23—3022no—
326C23—3021no—
327C23—6041no—
328C23—6041no—
329C23—1511no—
330C23—1511no—
331C23D4×D15111yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—3021no—
335Q8—3021no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—3021no—
340D4—3021no—
341D4—6042no—
342D4—6042no—
343D4—6042no—
344D4—6042no—
345D4—6042no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3022no—
352C2×C4—3022no—
353C2×C4—3022no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—6042no—
360C2×C4—6042no—
361C2×C4—1511no—
362C2×C4—1511no—
363C2×C4—1512no—
364C2×C4—1512no—
365C2×C4D4×D15111yescharacteristic
366C2×C4C23×D15111yescharacteristic
367C8—21no—
368C8—3021no—
369C8—1512no—
370C8D4×D15112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3021no—
378C22—3021no—
379C22—3021no—
380C22—3021no—
381C22—3021no—
382C22—6044no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—1512no—
387C22C2×D4×D15111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3021no—
393C4—6041no—
394C4—6041no—
395C4—6041no—
396C4—1512no—
397C4C2×D4×D15111yescharacteristic
398C4#41×D15111yescharacteristic
399C2—41no—
400C2—81no—
401C2—3022no—
402C2—6041no—
403C2—12081no—
404C2#121×D15111yescharacteristic
405C2#2375300811yescharacteristic
406C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
hypercenter#468D151
hypocenterC151#3054
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. C2×M16×D151C2semidirect
3. #23752725C2semidirect
4. #23752722C2semidirect
5. #23752469C2semidirect
6. #23752468C2semidirect
7. #23752464C2semidirect
8. #23752463C2semidirect
9. #23752459C2semidirect
10. #23752458C2semidirect
11. #23752455C2semidirect
12. #23752249C2semidirect
13. #23752207C2semidirect
14. #23752205C2semidirect
15. #468×C151C2semidirect
20. C2×#14558994C22semidirect
21. C2×#14558993C22semidirect
22. C2×#14558989C22semidirect
45. #18012673C22semidirect
46. #18012670C22semidirect
47. #18012670C22semidirect
48. #18012664C22semidirect
49. #18012663C22semidirect
50. #18012662C22semidirect
51. #18012661C22semidirect
52. #18012660C22semidirect
53. #18012659C22semidirect
54. C2×SD16×C151C22semidirect
58. #107×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
91. C8×D151D4semidirect
203. C151#3054semidirect
216. #468D151semidirect
226. C2×SD16C2×D151semidirect
254. #107C2×D151semidirect
260. #103C2×D151semidirect
264. #102C2×D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180127602
C2×M16×D1512
#237527252
#237527222
#237524692
#237524682
#237524642
#237524632
#237524592
#237524582
#237524552
#237522492
#237522072
#237522052
#468×C1512
#3054151